call someone out on something

call someone on something :

When someone makes a mistake or lies about something, you go "Hey, that's wrong, that's a lie." That is calling someone on something. To point out someone's mistake.

call someone out on something :

Quoting from an comment by Sarah Palin, "And Sen. Biden, I respected you when you called him out on that. You said that his vote was political and you said it would cost lives."

It seems that it means taking on someone about something.

Definition by reference.com:

call out
a. to speak in a loud voice; shout
b. to summon into service or action; Call out the militia!
c. to bring out; elicit; The emergency called out her hidden abilities.
d. to direct attention to with a callout: to call out each detail in an illustration
d. Informal. to challenge to a fight.

call-out
(n) a challenge to a duel

In case of Palin's comment, it was made to Joe Biden, who was her counterpart.